Blackbody simulator with uniform emissivity

ABSTRACT

A blackbody simulator which includes a core having a non-spherical cavity and an aperture to the cavity. A substantial portion of the cavity surface is shaped so that the value of the projected solid angle of the aperture with respect to any point of the cavity surface portion is approximately constant.

BACKGROUND OF THE INVENTION

1. Related Application

This is a continuation of application Ser. No. 06/340,808, filed on Jan.19, 1982, abandoned.

The present application is also a continuation-in-part of co-pendingapplication, Ser. No. 163,305, filed June 26, 1980 now U.S. Pat. No.4,317,042.

2. Field of the Invention

The invention relates to blackbody simulators, and more particularly tosuch simulators having a core with an aperture to an interior cavity,the aperture simulating the properties of a similarly sized and shapedblackbody.

3. Description of the Prior Art

A blackbody is an idealized object which would absorb allelectromagnetic radiation impacting it. Since such an object wouldabsorb all light striking it, it would appear black. The physicalproperties of blackbodies have been intensively studied. Although thedefinition of a blackbody is in terms of its perfect absorption ofelectromagnetic radiation, its most interesting properties areassociated with its radiated energy. When considered as a radiationsource, it is generally considered to be heated to increase its radiatedenergy. The total emission of radiant energy from a blackbody isexpressed by the Stefan-Boltzmann law, which states that the totalelectromagnetic emission of a blackbody is proportional to the fourthpower of its absolute temperature. The spectral energy distribution ofthe radiant energy emitted by a blackbody is expressed by Planck'sradiation formula. Planck's radiation formula indicates that a blackbodywhich has a temperature between 50 degrees Kelvin and 3,000 degreesKelvin will emit electromagnetic radiation principally in the infraredregion. This temperature range encompasses the temperatures at whichmost nonnuclear physical phenomena occur.

A blackbody is an idealized concept. A blackbody simulator is anapparatus designed to simulate the physical properties of the idealizedblackbody. A blackbody simulator is of great use in infrared researchand development and manufacturing. For instance, it may be used toprovide a source of infrared radiation of a known signal level and aknown spectral distribution. It may be used to provide a source ofinfrared radiation for the adjustment or testing of infrared components,assemblies or systems. Another use for blackbody simulators is as a nearperfect absorber of infrared radiation.

Intuitively, it would appear that a blackbody simulator would be merelyany black object. Such simulators have been used in the past, but theircorrespondence to a true blackbody has been poor. The best blackbodysimulators are formed by creating a cavity in a core material, thecavity forming an aperture on a side of the core. The aperture is usedto simulate a flat blackbody having the shape and size of the aperture.Particular cavity shapes are chosen to cause multiple reflection andeventual absorption of any electromagnetic energy entering the aperture.

One measure of the closeness by which a blackbody simulator approaches atrue blackbody is its emissivity. The emissivity of an isothermalsurface is the ratio of the radiation emitted by the surface to theradiation emitted under identical conditions by a blackbody having thesame shaped surface and temperature. Unless the blackbody simulator isluminescent, the emissivity of an isothermal blackbody simulator is lessthan one.

If the cavity surface coating of a blackbody simulator has an emissivityabove 0.7, most cavity shapes in commercial use in blackbody simulatorswill result in a device in which the on-axis emissivity of the aperturewill exceed 0.99.

The angular distribution of radiation from a perfectly diffuse radiator,such as a blackbody, is given by the Lambert cosine law. This law statesthat the signal level of radiation from a perfectly diffuse surface isproportional to the cosine of the angle between the direction ofemission and a normal to the surface. Accordingly, the Lambert cosinelaw provides a standard against which the uniformity of emission from ablackbody simulator can be compared against a blackbody.

It is well known how to manufacture a blackbody simulator with a cavityshape configured to have an on-axis emissivity very close to one. Thereare commercially available blackbody simulators with an on-axisemissivity of 0.9997. Unfortunately, the prior art cavity shapes forhigh emissivity blackbody simulators have been found to not provide theuniformity of emission specified by the Lambert cosine law. Suchuniformity of emissivity is becoming a significantly more importantconsideration in current infrared research and development. It appearsthat the uniformity of blackbody simulator emissivity will become asignificantly more important consideration in future manufacturingadjustments and tests of infrared components, assemblies and systems.

For instance, infrared viewing systems have been the subject ofintensive research and development. Initially, a single element infraredsensor was used with a two axis mechanical scanner to provide a twodimensional infrared picture. For calibration and testing of such singleelements, a blackbody simulator was used to illuminate a relativelynarrow field of view. Since a single element infrared sensor was used,uniformity of emissivity was not as important as it is today. However,infrared viewing systems now in development use a one dimensional or twodimensional array of infrared sensors, thereby eliminating the need forone direction or both directions of mechanical scanning. Testing andcalibration of such array detector systems require a blackbody simulatorwhich has an emissivity which is uniform over the appropriate angularfield of view.

Although emissivity and uniformity of emissivity are importantspecifications for a blackbody simulator, such simulators also aredeveloped with other very practical considerations in mind.

Key specifications for a blackbody simulator to be used as a source ofinfrared emission include aperture size and temperature range. The costof a black body simulator is in large part determined by the physicalsize and weight of the blackbody simulator. The cost is also affected bythe particular cavity shape used inasmuch as certain cavity shapes aremore expensive to manufacture.

The radiation properties of a cavity type blackbody simulator aredetermined by the size and shape of the cavity and the temperature,material and texture of the cavity walls. Most commercially availableblackbody simulators have a cavity shape based upon a cone. Otherpopular shapes are the sphere, the reentrant cone and the cylinder. Areentrant cone cavity has a shape which is formed by placing base tobase two circular cones having the same size base, and truncating theapex of one of the cones to form the aperture. Both a conical cavity andreentrant cone cavity have a conical apex opposite the aperture.

An advantage to a blackbody simulator having a spherical cavity is thatits emissivity is very uniform. Further, it has been theoreticallyproved and experimentally verified that the surface of a sphericalcavity tends to become isothermal, i.e., the cavity surface temperaturetends to become uniform. It is desirable for the surface of the cavityto be as nearly as possible isothermal since that property is necessaryfor the spectral distribution of the simulator to conform to the Planckradiation formula. Despite these advantages, a spherical blackbodysimulator is a large object, and is correspondingly very heavy. Inaddition, its on-axis emissivity can be achieved by consideredly smallerblackbody simulators having conical or reentrant cone cavities. Anotherdisadvantage to a blackbody simulator using a spherical cavity isspecular reflection from the cavity wall opposite the aperture.Radiation entering the aperture on-axis tends to be reflected out theaperture, rather than be absorbed. Such specular reflections areantithetical to the definition of a blackbody. This latter deficiency ofa spherical cavity blackbody simulator is sometimes overcome by using atilted or off center arrangement for the sphere and the core, but thistechnique requires even larger and heavier assemblies.

Blackbody simulators having a generally cylindrical cavity shape, withthe aperture in one axial end of the cylinder, are easy to manufacture.Some cylindrical cavities have been provided a concentrically groovedback plate where the grooves have a generally uniform saw toothcross-section, such as that shown in De Bell, U.S. Pat. No. 3,419,709.Unfortunately, cylindrically shaped blackbody simulators have loweron-axis emissivity than a cone, and they have poor uniformity oftemperature and poor uniformity of emissivity.

Most commercial blackbody simulators have a cavity shape which is eithera cone (such as that shown in McClune, et al., U.S. Pat. No. 3,275,829)or reentrant cone (such as that shown in Stein, et. al., U.S. Pat. No.3,699,343). Such shapes have excellent on-axis emissivity. Specifically,the apex of the cone opposite the aperture has emissivity much greaterthan that of a sphere with a diameter such that the wall of the sphereopposite the aperture would be at the same distance from the aperture asthat of the apex of a cone or a reentrant cone. A blackbody simulatorhaving a cone as a cavity shape is relatively easy to manufacture,except for the apex, but it has poor uniformity of emission. Thereentrant cone is more difficult to manufacture, but the advantage of areentrant cone over a simple cone is that the surface of the cavitymaintains a more uniform temperature and emissivity than that of asimilar sized cone, since a reentrant cone cavity tends to minimize thecooling of the cavity near the aperture.

It is an object of the invention to provide a cavity type blackbodysimulator that has the high on-axis emissivity obtained with cone orreentrant cone blackbody simulators, yet also approaching the uniformemissivity obtained with spherical blackbody simulators. Another objectof the invention is to provide a compact blackbody simulator which isshorter and smaller in diameter than a blackbody simulator having aspherical cavity with the same emissivity. Yet another object of theinvention is to provide a blackbody simulator with a cavity having ashape which tends to take a uniform temperature when heated. A furtherobject of the invention is to provide a method for the design of ablackbody simulator cavity having a specified maximum depth, diameter,and aperture size in which high emissivity and uniformity of emissivityare obtained.

SUMMARY OF THE INVENTION

These and other objects of the herein disclosed invention are providedby a blackbody simulator having a cavity shaped to insure that the valueof the projected solid angle of the aperture is constant orapproximately constant when viewed from all points on the cavitysurface, or alternately, when viewed from all points on the primaryradiating surface of the cavity. The primary radiating surface of ablackbody simulator cavity with respect to an object outside the cavityis the portion of the cavity surface which is in direct line of sight tosome portion of the object.

The projected solid angle of one surface as viewed from a second surfaceis proportional to the fraction of the total amount of radiant energyleaving the second surface that impinges on the first surface.

In one embodiment, the cavity shape is determined by assuming that theaperture is sufficiently small so that it would be unnecessary toperform an integration over the aperture to compute the projected solidangle, thereby simplifying the calculations necessary to determine thecavity shape. For an apex half angle less than 60 degrees, a suitablecavity shape is described which has a cross-sectional shape described bya smoothly curved line forming a half angle at the aperture ofapproximately one half the apex half angle. The maximum cross-sectionalradius of this embodiment is generally reached at approximately 58% ofthe distance from the aperture to the apex.

In another embodiment, the cavity determined by the above describedembodiment is truncated near the aperture end to form a larger aperture.For instance, the diameter of the aperture formed by the truncation maybe approximately one half of the maximum cross-sectional diameter of thecavity.

In another embodiment, numerical integration techniques have been usedto determine a series of cavity shapes which maintain essentiallyconstant the projected solid angle of a circular aperture with respectto each portion of the cavity surface. The simplest shape is formed bythree smoothly arcuate subsurfaces. The first subsurface forms acone-like apex opposite the aperture, the subsurface smoothly curving asit approaches the aperture until its tangent intersects the aperture.The second subsurface starts from the rim of the aperture and proceedstoward the apex; it is a portion of the surface of a sphere. The thirdsubsurface arcuately joins the two previously described subsurfaces. Inanother embodiment, the three subsurfaces of the above describedembodiment are identified. Then the second and third subsurfaces areinterrupted at some specified maximum distance off axis. The second andthird subsurfaces are then connected by a series of subsurfaces thatappear in cross-section somewhat like a tilted sawtooth shape. Thesesubsurfaces are all maintained with an off axis distance less than orequal to the specified maximum off axis distance; and the surfacedetails of these subsurfaces are all determined so that the projectedsolid angle of the aperture as seen from all points on all thesesubsurfaces is contant and equal to the projected solid angle of theaperture as seen from all points on the first, second and thirdsubsurfaces.

In the embodiment just described, the multiple subsurfaces aremaintained with a specified maximum off-axis distance, and thesemultiple subsurfaces are located on the side walls of the cavity. Inanother embodiment, these multiple subsurfaces begin at the apex andcarry around from the apex to the aperture.

If the inventive blackbody simulator is to be used to subject a specificutilization apparatus or volume or area to electromagnetic flux, thecavity surface may be modified for ease of manufacturing in any of anumber of ways that will insure that the primary radiating surface ofthe cavity with respect to the utilization object or volume or area is asurface in which the projected solid angle of the aperture with respectto each point on the primary radiating surface remains essentiallycontant. Other portions of the cavity surface may be shaped to reducethe size, weight, and cost of the blackbody simulator.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic cross-section of the cavity of a blackbodysimulator, illustrating the geometrical aspects involved in defining theprojected solid angle of a small area on the aperture with respect to apoint on the cavity surface.

FIG. 2 is a diagrammatic cross-section of a blackbody simulator similarto FIG. 1, illustrating the primary radiating surface of the cavitysurface with respect to an object or volume or area which will utilizeradiation emitted from the aperture.

FIG. 3 is a graph of a curve defining the surface of a rotationallysymmetrical cavity of a preferred embodiment in which the size of theaperture is assumed to be very small with respect to the axis ofsymmetry.

FIGS. 4A-4D illustrate cross-sections of embodiments of the invention inwhich by numerical integration the projected solid angle of a finitesized aperture is held constant with respect to the primary radiatingsurface of the cavity for FIG. 4B and with respect to all points on thecavity surface for FIGS. 4A, 4C and 4D.

FIGS. 5A-5F illustrate cross-sections of several embodiments of theinvention where multiple subsurfaces have cross-sections lying betweenseveral different alternative pairs of inner and outer limiting curves.

DESCRIPTION OF PREFERRED EMBODIMENTS

Although the radiation properties of a blackbody are well defined by theearlier mentioned Stefan-Boltzmann law and Planck radiation formula, theradiation properties of blackbody simulators are not so tidilysummarized. Numerous articles have been published which attempt todescribe or define the radiation of a blackbody simulator having aspecified cavity shape. In order to reach any useful conclusions,numerous simplifying assumptions are made in the published theories ofblackbody simulators. In general, the theoretical studies of blackbodysimulators have used as a figure of merit for a blackbody simulator itson-axis emissivity. More recent theoretical studies, such as "Emissivityof Isothermal Spherical Cavity with Gray Lambertian Walls", by F. E.Nicodemus, Appl. Opt., Vol. 7, No. 7, pps. 1359-1362, July, 1968, havebeen concerned with the angular uniformity of emissivity of a blackbodysimulator. Experimental studies of blackbody simulators having cavityshapes which are spherical, conical, or cylindrical have demonstratedthat the commonly used conical and cylindrical cavity shapes do not havethe angular uniformity of emissivity which a true blackbody would have.Such experimental work is described, for instance, in "Cavity RadiationTheory" by F. O. Bartell and W. L. Wolfe, Infrared Physics, 1976, Vol.16, pps. 13-24.

As described in this second paper, the experimentally measurednon-uniformity of emission of blackbody simulators may be explained byconsidering the effect of the projected solid angle formed by theaperture with respect to the cavity surface.

Experimental and theoretical studies have demonstrated that for a givencavity depth, i.e., distance along a perpendicular to the aperture tothe furtherest position of the cavity surface, a spherical cavity willhave lower but more unifrom emissivity than a concial cavity when bothare used as blackbody simulators.

The inventive cavity shapes for blackbody simulators are based on theconcept that opposite the aperture a conical apex will provide highemissivity, and that this high emissivity can be maintained across otherpositions of the cavity surface by a cavity surface which is shaped toassure that the projected solid angle of the aperture with respect toeach portion of the cavity surface takes the same value as it does atthe apex. Standard numerical integration techniques have been used todetermine cavity shapes for a family of blackbody simulator cavities inwhich uniformily high emissivity may be expected.

There are two concepts of principal importance in the description of theinventive blackbody simulator cavities. They are that of the projectedsolid angle and that of a primary radiating surface for a cavity.

FIG. 1 diagrammatically illustrates a cross-section of a blackbodysimulator core 101. The core 101, as will be described in more detailbelow, is of a material such as metal, graphite, or ceramic which maywithstand the temperatures to which it will be heated to generate thedesired radiation. On one side of the core 101 is an aperture 102 to aninterior cavity 103. For minimum size, weight, complexity, and costs,cavities in blackbody simulators generally have rotational symmetry orare composed of subcavities which are each rotationally symmetrical.There are exceptions to this general rule of axial symmetry. For examplethe core or cavity of a spherical cavity blackbody simulator may beoriented in a tilted or off center way so the total system optical axisintersects the back wall of the sphere at a nonperpendicular angle. Theaperture 102 is typically a circle, although other aperture shapes maybe easily provided for by placing a suitable plate having a cut-out ofthe desired shape in the aperture or in front of the aperture.

Aperture 102 has diameter D. Line 104 is the axis of rotational symmetryof the cavity 103. L is the depth of the cavity as measured along therotational axis 104 from the aperture 102.

Such a blackbody simulator provides apparent blackbody radiation fromthe aperture 102 as though it were a true blackbody located at theaperture and having the shape and size of the aperture 102. (Of course,a true blackbody radiates energy in all directions, unlike a blackbodysimulator cavity which radiates simulated blackbody radiation onlywithin a limited angular field measured from the rotational axis 104).

The projected solid angle may be described as follows. Let S₁ designatethe surface 106 of the cavity 103, with s₁ a point on S₁. Let the figureformed by the aperture 102 be designated S₂ and let a point on S₂ bedesignated s₂. Let d=d(s₁,s₂) be the length of the line 107 between s₁and s₂. Let r be the distance from s₁ to line 104, and let z be thepoint on line 104 at which a perpendicular to line 104 will intersects₁. Line 109 is the tangent to the cavity surface 106 at s₁. Line 110 isthe normal to the cavity surface 106 at s₁. Line 108 is the normal tothe aperture 102 at s₂. Let A₁ be the angle formed between lines 107 and110, and let A₂ be the angle formed between lines 107 and 108.

The projected solid angle of the aperture 102 with respect to point s₁on S₁ is given by the formula ##EQU1## As is well known, the projectedsolid angle of a second surface with respect to a first surface isproportional to the fraction of the total amount of radiant energyleaving the first surface that impinges on the second surface. If auniform cavity surface is at a uniform temperature, i.e., the surface isisothermal, and if the projected solid angle of the aperture withrespect to any portion of the cavity surface is constant, the radiationfrom each cavity surface portion through the aperture will also beconstant. Therefore, such a uniformly heated cavity surface will tend tostay at a uniform temperature since each portion of the cavity surfacewill suffer the same energy loss through the aperture.

FIG. 2 illustrates the concept of a primary radiating surface for ablackbody simulator cavity. In FIG. 2, a blackbody simulator core 101ais shown in crosssection. The blackbody simulator is assumed to be usedto radiate electromagnetic radiation 201 from the aperture 102a ontosome utilization object or volume or area 202. For instance, theblackbody simulator may be providing infrared radiation to an infraredoptics system. The primary radiating surface of the cavity surface 203is that portion of the cavity surface 203 which is in direct line ofsight through the aperture 102a to some portion of the utilizationobject or volume or area 202. In FIG. 2, this would include that portionof the cavity surface 203 from point 204 around to the rear 205 of thecavity surface to point 206. The primary radiating surface of a cavityis therefore that portion of the cavity surface which may directlyradiate enery onto some portion of the utilization object or volume orarea 202.

The importance of the concept of the primary radiating surface is thatit is this portion of a blackbody simulator cavity surface whichprincipally determines the emissivity and uniformity of emissivity ofthe blackbody simulator. If it is known what uses would be made of ablackbody simulator, i.e., what the utilization objects will be, andtheir planned distances from the aperture of the blackbody simulator,the inventive blackbody simulator cavity shapes may be designed toprovide the desired high emissivity and uniformity of emissivity, as maybe measured at the utilization objects. As is clear from FIG. 2, thecloser a utilization object or volume or area 202 approaches theaperture, the larger the primary radiating surface will be. If it is notknown what use will be made of a blackbody simulator, then a largerprimary radiating surface will provide a device with greaterversatility.

Inasmuch as the inventive cavity shapes are rotationally symmetricalabout an axis, in order to describe the cavity shapes, it is sufficientto specify a process for determining a radius of the cavity at allpositions on the rotational axis. Therefore, the inventive cavity shapeswill be described in terms of a two dimensional graph of a functionwhich, if "rotated" about the rotational axis will form the inventivecavity shape.

The inventive cavity shapes have not been susceptible to description bya mathematical formula. Numerical approximation techniques have beenused to determine the cavity shapes.

Each of the inventive cavity shapes will be described in terms of a"normalized form" which assumes that the depth of the cavity is unityand the diameter of the aperture is D. Proportional reduction orexpansion of a normalized cavity shape will allow manufacturing of acavity of any arbitrary depth.

Each of the inventive cavity shapes has a conical apex opposite theaperture. A₀ will be used to designate the apex half angle, i.e., theangle formed between the axis of rotational symmetry and the tangent tothe cavity surface at the apex. As is well known, a conical apex in arotationally symmetrical blackbody simulator cavity generates highemissivity along the axis of symmetry. The inventive cavities will beshaped so that the high emissivity of the apex will be uniformlygenerated by all portions of the cavity surface or at least thoseportions which directly radiate energy onto utilization objects.

As with the cavity in most commercial black body simulators, theinventive cavity shapes are rotationally symmetrical and are for usewith a circular aperture. It will be obvious to one skilled in the artthat the methods to be described below can be extended to define cavityshapes terminating in any arbitrary shape aperture. However, thepractical difficulties in manufacturing cavities according to theteachings of the invention which will have a non-circular aperture tendto discourage production of blackbody simulators with such apertures.The convential approach to providing a simulator for a non-circularblackbody is to insert a plate having a suitably shaped cut-out betweena blackbody simulator having a circular aperture and whatever apparatuswill be subjected to the radiation emitted from the blackbody simulatoror alternatively to place such a plate in the cavity aperture.

The apex half angle is a fundamental parameter in the definition of aspecific cavity shape. Each of the embodiments of the inventiondescribed below define a family of cavity shapes which have as one ofits parameters the apex half angle. The choice of a particular apex halfangle for a cavity is made in part by reviewing the shapes which resultfrom that choice to determine if the resulting maximum radial crosssection will result in a blackbody simulator having an acceptable sizeand weight for the intended purposes.

FIG. 3 is a graph of a function illustrating one of the "small aperture"embodiments of the inventive blackbody simulator cavity shapes. Asdiscussed above, it is assumed that the axis of symmetry 104 is one unitlong, with z=0 at the aperture 102 and z=1 at the apex end.

The small aperture cavity shapes are determined by assuming that theaperture 102 is sufficiently small with respect to the length of theaxis of symmetry 104 so that the integral specified in Equation 1 may besimplified by assuming that for each point s₁ on S₁, the quantities A₁,A₂, and d will be effectively constant during the integration over S₂.

As mentioned, the inventive cavity shapes are based on the concept thatmaximum uniform emissivity should be generated by a cavity shape inwhich the projected solid angle of the aperture with respect to pointson the primary radiating surface of the cavity is held constant. Thesmall aperture embodiments assume the entire cavity surface is theprimary radiating surface.

Using the mathematical terminology previously introduced (summarized inTABLE 1), under the simplifying small aperture assumption, at the apex,the projected solid angle of the aperture 102 will be ##EQU2## since theaperture 102 is perpendicular to the axis of symmetry 104. Therefore,since the projected solid angle of the aperture as seen from all cavitysurface locations is a constant, then with respect to any other points₁, the projected solid angle of the aperture will be ##EQU3## AssumingA₁, A₂, and d will not vary during the integration over S₂ leads to thefollowing simplification of Equation (3): ##EQU4## Further, under oursimplifying assumption, d² =z² +r².

Let line 111, shown in FIG. 1, be parallel to the axis of symmetry 104and pass through s₁. Let A'₁ be the angle formed between lines 111 and109, i.e., the angle of the tangent at s₁ with respect to the axis 104.Then A'₁ +A₁ +A₂ =90°. After further observing that A₂ =arctan(r/z),Equation 4can be further simplified to: ##EQU5##

Equation 5 is an equation which is susceptible to solution by numericalapproximation techniques. At the apex, r=0,z=1, and A'₁ =A_(o). Anarbitrary set of points on the axis of symmetry 104 is chosen for whichthe corresponding cross-section radius will be computed. For instance,assume the cross-sectional radius will be determined for z=1.00,0.99, .. . , 0.01,0.00. Starting at the apex, i.e. z=1.00, the tangentspecified by A'₁ is followed up until it intersects the lineperpendicular to the axis of symmetry determined by z=0.99, therebydetermining a tentative corresponding value for r when z=0.99. A'₁ atz=0.99 may be computed by use of Equation 5.

To improve the accuracy of the curve which satisfies Equation 5, thevalue of A'₁ which was computed should be averaged with A₀ and from thisaverage, a second r value is determined for z=0.99 From this second rvalue a second A'₁ value can be computed. This second A'₁ value shouldnow be averaged with A_(o), and from this new average, a third r valueis determined for z=0.99. This iterative process should be repeatedseveral times to improve the numerical accuracy of the r and A'₁ valuesfor z=0.99. which satisfy Equation 5.

The values of r and A'₁ when z=0.98 is determined in a similar mannerfrom the values of A'₁ and r for z=0.99. Continuing this process insequence for each of the chosen points on the axis defines a curve asshown in FIG. 3.

Table 2 lists the values of an embodiment of the invention determinedwith respect to the small aperture assumption when the apex half angleis 30 degrees. All cavity shapes determined by the described method haveresulted in very small r when z=0, with smaller r for smaller values ofA_(o). When A_(o) has been 20° or less, it has been r=0.0±0.00001 whenz=0.0; and when A_(o) has been as large as 88°, it has been r=0.0±0.001when z=0.0.

Table 3, lists the maximum cross-sectional radii and corresponding zvalues which have been determined for various apex half angles. A'₂ isthe aperture half angle, i.e., the angle formed with respect to the axisof symmetry 104 by the tangent to the cavity surface S₁ where it meetsthe aperture, i.e., z=0.

As indicated in Table 3, the inventive small aperture cavity shapes arecharacterized by having A'₂ approximately -A₀ /2 and the maximum crosssectional radius occurring near r=0.58 if A₀ is not greater than 60degrees. As shown in FIG. 3, the small aperture cavity embodiments havea smooth shape, except at the apex and aperture.

The cavity shapes determined by the above described process are not ofpractical interest unless an aperture of useful size is provided, sothat radiation may be emitted.

Satisfactory results may be expected by truncating the curve definingthe cavity at z between 0.01 and 0.31, and possibly at higher values, toform the aperture. Analogizing to the most popular designs for reentrantcone cavities, the preferred embodiments of the inventive small aperturecavities will truncate the curve at the point near the aperture thatwill result in an aperture radius which will be approximately 1/2 themaximum cross-sectional radius.

Use of a more sophisticated numerical approximation technique, in whichthe integration over S₂ is approximated by a finite sum, allowsdetermination of other inventive cavity shapes without the necessity ofthe small aperture assumptions which led to Equation 5. FIG. 4A is across-section of an illustrative cavity shape of a "three surface"finite aperture embodiment of the invention in which the integral overS₂ is computed in determining the aperture's projected solid angle withrespect to points on the cavity surface S₁.

As previously discussed, it is assumed that the aperture is circularwith diameter D.

Numerical integration techniques approximate an integral over a surfaceby a finite sum, each term of the sum approximating the integral over asmall portion of the surface. In the present invention, the surface S₂of the circular aperture has been approximated by several grids ofelements. The more elements in this grid (i.e., the finer the grid), andthe more closely the grid approximates S₂, the more accurate theapproximation to the projected solid angle of the aperture with respectto points on the cavity surface S₁.

Table 4a lists the x-y coordinates for the centers of a set of 57squares which form a grid approximating a circular aperture withdiameter D=8.52. Each square will have area 1. In order to compute theprojected solid angle of S₂ with respect to a point s₁ on S₁, theintegrand of Equation 1 is computed with respect to the centers of eachof the squares. It is assumed that the values of A₁, A₂, and d will notsignificently vary over the small grid elements, and that therefore theprojected solid angle of the aperture will correspond to the sum overthe 57 squares.

Although Table 4a lists the coordinates for a grid of 57 squaresapproximating a circular aperture with D=8.52, the coordinates of thisgrid may be scaled to approximate a circle with diameter D' by merelymultiply each x and each y coordinate by D'/8.52.

Table 4a should not be construed to imply that preferred embodiments ofthe invention would have L/D=1/8.52. In actuality, useful cavity shapeshave an L/D ratio of from less than 1/1 to more than 50/1 with mostratios between about 2/1 and 10/1. Table 4a is only meant to specify themanner in which a circular aperture may be approximated by a grid ofelements. The coordinates of the grid elements of Table 4a may be scaledas necessary to provide any desired L/D ratio.

An alternate grid of elements approximating a circle of diameter D=8.20is provided by 61 hexagonal elements with centers having x-y coordinatesas listed in Table 4b. The elements are tightly arranged in a hexagonalarray. The hexagonal elements each have opposite sides separated by adistance of 1. The x-y coordinates of this array may be also scaled asnecessary to approximate an aperture with any specified diameter toobtain a cavity with any desired L/D ratio.

It will be obvious to those skilled in the art that the grid arrays ofTables 4a and 4b are arbitrary approximations to a circular aperture,and that similar results will be obtained by substituting any other gridof elements that approximate the aperture's shape. Further, themodifications necessary to approximate non-circular apertures areequally obvious to those skilled in the art.

It has been found that the cavity shapes which result from a numericalintegration with respect to a grid of 57 squares based on Table 4a arein close agreement to those which are computationally based on ahexagonal grid of 61 elements based on Table 4b. It is not theparticular grid which determines the inventive cavity shape, but thesize of the aperture being approximated by the grid. Two other gridshave been useful for this invention. The seven innermost points of Table4b, (0,0), (0,±1), (±0.5√3,±0.5) have been used to obtain approximateresults with a Hewlett Packard Model 41C handheld calculator. Thetwenty-one innermost points of Table 4a, (0,0), (0,±1), (±1,0), (0,±2),(±2,0), (±1,±1), (±1,±2), (±2,±1), have been used to obtain cavityshapes that are in close agreement to those based on all 57 points ofTable 4a.

The embodiments of the invention based on a numerical integration overthe aperture result in a cavity surface having an axial cross-sectionwith the general appearence of the curve of FIG. 4A. As previouslymentioned, in determining a particular cavity shape, one parameter isthe apex angle A₀. For the inventive finite aperture cavity shapes,another parameter is D, the aperture diameter, or more precisely the L/Dratio. Since the normal form for describing the inventive cavity shapeshas L=1, an aperture diameter D allows direct conversion to thecorresponding L/D ratio.

Once A₀ and D have been specified, the following method may be used todetermine a cavity shape in which the projected solid angle over theaperture 102 with respect to points on the cavity surface 106 isconstant.

As before, it is assumed that the axis of symmetry has length L=1. Itcan be proved that a spherical cavity with diameter [1+(sin(A_(o)))(D²/4)]/√sin (A_(o)) having a circular aperture of diameter D will have aprojected solid angle of its aperture with respect to all points on thecavity surface that is identical to the projected solid angle of thesame aperture with respect to a conical apex opposite the aperture atz=1 with half angle A₀.

Further, it can be proved that the projected solid angle of an apertureon a spherical cavity with respect to any point on the cavity surface isconstant. In other words, spherical shaped cavities may be considered tobe a limiting case for the inventive cavity shapes as A₀ approaches 90degrees.

The importance of these observations are that, given a conical apex atz=1, a first portion 401 of the cavity surface near the aperture 102 maybe defined by a sphere 400 with diameter [1+(sin(A_(o)))(D²/4)]/√sin(A_(o)). The projected solid angle of the aperture with respectto any point on this first subsurface 401 will be the same as is at aconical apex at z=1 with half angle A₀.

Numerical techniques are used, in a manner similar to that describedearlier with respect to the small aperture embodiments, to incrementallyextend the conical apex from z=1.00 toward z=0. Unlike the smallaperture embodiments, for each z value for which an r value will bedetermined, a numerical integration over the aperture surface must beperformed. Nevertheless, the numerical approximation techniques todetermine successive cross-sectional radii and tangents for decreasing zvalues is straightforward, although computationally lengthy.

More specifically, at z=1.00, r=0, Equation 1 can be used to determinethe projected solid angle of the aperture at the apex by summing overthe elements in the grid rather than integrating over S₂, with theintegrand of Equation 1 determined for each grid point, and with dS₂replaced by the area of each element. A straightforward computationallows a determination of A₁, A₂, and d for each grid element withrespect to the apex.

The tangent at the apex can be extended until it intersects the lineperpendicular to the axis of symmetry at z=0.99, or whatever z valueclose to the apex for which the cross-sectional radius is next to becomputed. Using A₀ as a first approximation for determining the r valueat this second Z value, by standard interpolation and iterativetechniques similar to those described earlier, the finite sum version ofEquation 1 may be solved to determine corresponding A'₁ and r values forthe chosen z value such that the projected solid angle of the apertureremains the same as it was at the apex.

The process may be continued step by step for z=1.00 toward z=0, therebydefining a second subsurface 402 of the cavity which extends the conicalapex in a manner to hold constant the projected solid angle of theaperture 102 with respect to each point on this second subsurface 402.

For each finite aperture cavity shape embodiment which has beendetermined by this numerical integration techinque, there is a point Xon this second subsurface 402 which for most practical cavities has a zvalue between z=0.50 and z=0.20, in which the tangent 403 of the cavitysurface at this point intersects the rim of the aperture. When thisoccurs, the second subsurface 402 of the cavity surface cannot befurther continued since to continue it would define a cavity shape inwhich previously defined portions of the second cavity subsurface 402would not be in direct line of sight of all of the aperture. Such anoccurance would violate the conditions of determination of the previouspoints where it was assumed those previous points were in direct line ofsight of the entire aperture.

A third subsurface 404 of the finite aperture cavity surface embodimentjoins the second subsurface 402 to the first subsurface 401, therebycompleting the cavity shape. It is determined in the following way. Atpoint X on the second subsurface 402, a line 405 is drawn whichintersects the rim of the aperture at a point opposite the point on theaperture at which the tangent 403 to subsurface 402 at X intersects theaperture. This line 405 is assumed to approximate a tangent to the thirdsubsurface 404 at X in which the third subsurface 404 is moving awayfrom the aperture.

This tangent 405 is used to define an initial guess of a small portionof the third subsurface 404. A point on this line 405 is chosen near Xto define an initial guess for a new value of z and r. An appropriatetangent at this point is then calculated by the previously discussednumerical integration and approximation techniques.

An average tangent is then calculated which is half way between thetangent just calculated and the initial guess tangent 405. This averagetangent is then used in place of tangent 405 to find a second guessvalue of z and r. From the new z and r a new calculated tangent isdetermined. By iteration, final values of z and r are found. The point Xis the last point on subsurface 402 and the first point on subsurface404. The point (z,r) just found is the second point on subsurface 404.Successive points on subsurface 404 are then determined the waysuccessive points on subsurface 402 were found.

This process continues until the third subsurface 404 intersects thefirst subsurface 401. The curve of FIG. 4A is illustrative of theresulting cavity cross-section for such a "three surface" finiteaperture embodiment. For many parameter combinations of A_(o) and L/Dthat are of practical interest, the tangent to subsurface 404 isapproximately perpendicular to the axis of rotational symmetry 104 atthe point where subsurface 404 intersects the first subsurface 401.Table 5 lists the z and r values for such a "three surface" finiteaperture embodiment in which A₀ =45° and D=0.1 (with L=1, of course).

Although the method described to determine a finite aperture cavityshape embodiment results in a cavity shape in which the projected solidangle of the aperture is constant with respect to any point on thecavity surface, there is a disadvantage to these "three surface" finiteaperture embodiments in that the maximum radial cross-section mayapproach that of the sphere used to define the first subsurface 401.Although the embodiments are shorter than the sphere, it would also bedesirable to reduce the maximum cross-sectional radius, thereby reducingthe size, weight, and cost of the resulting black body simulator.

The simplest approach to obtaining a more commercially practical finiteaperture cavity shape is to relax the requirement that the aperture'sprojected solid angle be constant with respect to all points on thecavity surface. By requiring the projecting solid angle to be constantonly over a cavity's primary radiating surface, significant economicsmay be obtained. It is believed that such a requirement will notseriously affect the high uniform emissivity of a blackbody with acavity so simplified since the devices receiving the radiation emittedfrom the aperture will not be in the line of sight of the cavityportions in which the projected solid angle is not held constant.

FIG. 4B illustrates several simplifications of the cavity shape of FIG.4A. In each such cavity shape, it is assumed that there is no materialdeviation from the cavity shape of FIG. 4A over the primary radiatingsurface.

Line 410 provides a cavity in which the cavity shape of FIG. 4A ismerely truncated beyond a certain maximum radius. This results in acavity having a cylindrical portion between the first and secondsubsurfaces of FIG. 4A.

Line 411 truncates the curve of FIG. 4A at a maximum cross-sectionalradius, which is extended to the plane of the aperture, therebyresulting in a cavity in which the cavity portion near the aperture iscylindrical with the aperture on the axial end of the cylinder.

Of course, rather than having a cavity shape with the previouslydescribed first subsurface 401 of FIG. 4A, the cavity may be extended ina cylindrical manner from a point on the third subsurface 404 to theplane formed by the aperture 102, as indicated by line 412. Such anembodiment may not materially reduce the maximum cross-sectional radius,but does offer economics in manufacturing since the curved firstsubsurface 401 of FIG. 4A is avoided.

Other simplications to the finite aperture embodiments will be obviousto those skilled in the art. So long as the projected solid angle of theaperture with respect to the primary radiating surface is constant orapproximately constant, the approximately uniform and high emissivity ofthe inventive cavity shapes will be assured.

FIG. 4C illustrates one of a series of "Fresnel" embodiments of theinventive blackbody cavity shapes. The Fresnal embodiments are avariation on the finite aperture embodiments. Each Fresnel embodimenthas as design parameters A₀, the apex half angle, D, the aperturediameter, and M, the maximum desired cross-sectional radius. For FIG.4C, A_(o) =50°, D=0.25, and M=0.35.

A Fresnel cavity shape embodiment defines first 401 and second 402subsurfaces in the same manner as a finite aperture embodiment with thesame A₀ and D. The third subsurface 404 is extended only to point X',where r=M. At this point, a fourth subsurface 420 is determined whichapproaches z=0 again. The initial tangent 421 to the fourth subsurface420 at X' may be satisfactorily approximated by ensuring that thetangent 421 at X' forms the same angle with respect to a line 422 fromX' to the center of the aperture 102 that the tangent 423 of subsurface404 at X' forms with line 422.

This fourth subsurface 420 is continued in a similar manner as was donewith the second subsurface 402 until it intersects the first subsurface401 or its tangent 424, say at X", intersects the aperture. At X", afifth subsurface 425 is defined in a manner analogous to the thirdsubsurface 404.

This computational determination of subsurfaces continues until one ofthe subsurfaces intersects the first subsurface 401, resulting in a"Fresnel" version of a finite aperture embodiment in which the maximumcross-sectional radius is limited to a maximum value M, yet for whichthe projected solid angle of the aperture is constant with respectpoints on each of the subsurfaces.

The "tilted sawtooth" configuration of the Fresnel portion 426 of thecavity surface of FIG. 4C may be satisfactorily approximated by athreaded cavity shape which does not materially differ from the computedshape.

The tilted sawtooth configuration of the Fresnel portion 426 of thecavity surface of FIG. 4C and the threaded cavity shape which wasmentioned as a variation to FIG. 4C suggest worthwhile variations to thecavity shapes shown in FIG. 4B. Lines 410, 411, and 412 of FIG. 4Bprovide cavity shapes with cylindrical parts. Those cylindrical partsmight to be replaced by a tilted sawtooth, tilted thread design, or amore conventional thread design. Such replacements of the cylindricalparts might be performed with relatively small increases in complexityand with appreciable improvements in the approximation of these cavitiesto cavities which have the projected solid angle of the aperture aconstant when viewed from all points on the cavity surface. FIG. 4C withA_(o) =50°, D=0.25 and M=0.35 is useful to describe the general class ofFresnel embodiments of the inventive blackbody cavity shapes. However,the relatively large areas of subsurfaces 404 and 420 tend to make thisa less suitable design for most applications.

FIG. 4D shows a cross-section of a full cavity and core of a Fresnelembodiment. For FIG. 4D, A_(o) =76.5°, D=0.385 and M=0.40. Table 6 liststhe corresponding coordinate values. The relatively large area ofsubsurface 402 and the relatively large value of D make this anattractive design for many applications.

FIG. 4C and 4D show that the sequence of points X,X^(II), X^(III), . . .X^(V) (for FIG. 4D) or X^(XII) (for FIG. 4C) form an arch 430. As theparameter M varies, the X points move back and forth on this arch, butthe arch, and especially its maximum distance from the axis of symmetry104, remain approximately constant. This maximum distance of the archfrom the axis of symmetry 104 is important in the selection of the valueof M. If M is closer to this maximum distance of the arch from the axisof symmetry 104, there will be more and smaller "teeth" in the cavitycross-section, somewhat like FIG. 4C. If M is farther from this maximumdistance of the arch from the axis of symmetry 104, there will be fewerand larger "teeth", more like FIG. 4D.

The maximum value of M is the distance from the axis of symmetry 104 tothe place where subsurfaces 404 and 401 would intersect if they were notinterrupted. The minimum value of M is the maximum distance of the archfrom the axis of symmetry 104, because points inside the arch cannothave the same projected solid angle of the aperture as do the otherpoints on the cavity wall surface. If such a small value of M isnevertheless desired, then a different embodiment of the inventivecavity could be employed according to FIG. 4B, where the projected solidangle of the aperture is maintained constant only where viewed frompoints on the primary radiating surface.

Thus, it is seen that the arch 430 and the sphere 400 define a region ofsubsurfaces. Additional examples of cavity subsurfaces within the regionof subsurfaces are shown in FIGS. 5A-5F. These illustrate cross-sectionsof several embodiments of the invention having aperture half-angles lessthan 60°. In each of these embodiments, the cross-sectional curve of thecavity shape lies between a pair of inner and outer limiting curves,both of which lay within the region of subsurfaces.

FIG. 5A shows a cross-section of a cavity shape embodiment having anapex half-angle of 13°. A first subsurface 510 extends from the apex 507to the inner limiting curve which in this case is an arc 530 which isdefined in a manner similar to that of arch 430 of FIG. 4C. Accordingly,a tangent to the surface 510 at point Y intersects the rim of theaperture 506.

A second subsurface 511 extends from the intersection of the surface 510with the arch 530 at point Y to the outer limiting curve 508 which is astraight line passing through the apex 507 and perpendicular to theaxis. The outer limiting curve 508 is placed a distance N of 1.0 fromthe plane of the aperture 506.

Extending from Y' (the point at which the subsurface 511 intersects theouter limiting line 508), a third subsurface 512 extends to the innerlimiting curve 530 until the tangent to the subsurface 512 intersectsthe rim of the aperture as indicated at Y". This computationaldetermination of subsurfaces continues until subsurface 518 intersectsthe inner limiting curve 530. In order to reduce the overall width ofthe cavity, the next subsurface 519 extends from the inner limiting arch530 to a second outer limiting curve 509 which is a straight lineparallel to the axis at a distance M (which is 0.6 in this embodiment)from the axis of symmetry. The computational determination of thesubsurfaces then continues in a manner similar to that described forFIG. 4C and 4D until one of the subsurfaces (subsurface 529) intersectsthe subsurface 401 described in connection with FIGS. 4A-4D. Each of thesubsurfaces of the cavity of FIG. 5A are characterized by the fact thatthe projected solid angle of the aperture with respect to thesubsurfaces remains constant from each point on the subsurfaces. Table 7lists a representative set of z and r coordinates for the subsurfaces ofthe cavity of FIG. 5A.

An alternative embodiment is shown in FIG. 5B, which resembles theembodiment shown in FIG. 5A except that the perpendicular outer limitingcurve 508 of FIG. 5A is replaced by a slanted straight line outerlimiting curve 550 which makes an arbitrary 63° angle with theperpendicular axis through the apex. The inner limiting curve 580 isalso an arch similar to the arches 530 and 430 of FIG. 5A and 4C,respectively. Accordingly, the tangents to the subsurfaces at the arch580 intersect the rim of the aperture 506. The remaining outer limitingcurve is again the line 509 parallel to and spaced a distance of 0.6from the axis of symmetry. The resulting subsurfaces are less deep andsomewhat more uniform in cross-section than those shown in FIG. 5A. Arepresentative set of coordinates for the subsurfaces of the cavity ofFIG. 5B is listed in Table 8. This embodiment has an apex halfangle of15°.

The cavity shape represented by the outline shown in FIG. 5C is alsosimilar to that shown in FIG. 5A. Here however, the inner limiting arch530 of FIG. 5A has been replaced by a pair of perpendicular lines 601and 602 parallel to the outer limiting lines 508 and 509, respectively.The outer limiting line 509 is placed a distance of 0.65 from the axisof symmetry and the inner limiting line 602 is placed at a distance 0 of0.55 from the axis. The other inner limiting line 601 is placed adistance P of 0.85 from the aperture. As seen in FIG. 5C, thisembodiment may conveniently be fabricated with a backwall plate andsidewall cylinder as starting materials from which the subsurfaces maybe machined. The embodiment of FIG. 5C has an apex half angle of 20°.Representative coordinates for the subsurfaces are listed in Table 9.

Combining elements of the previous three embodiments, FIG. 5D shows acavity outline in which the inner and outer limiting curves 508 and 601of FIG. 5C are replaced by slanted straight line inner and outer curves650 and 651. The lines 650 and 651 are slanted at an angle of 68° withrespect to the perpendicular. The apex half angle of the embodiment ofFIG. 5D is 21°. Table 10 lists representative coordinates for thecross-sectional outline of this embodiment.

FIG. 5E shows an embodiment having an outer limiting curve 701 definedby a circle having a radius of 0.6 with a center indicated at 702 whichis at a distance of 0.4 from the aperture. The inner limiting curve 703is also defined by a circle having a radius of 0.45 with the same center702. The embodiment of FIG. 5E has an apex half angle of 20° and thesubsurfaces are represented by the coordinate points listed in Table 11.

FIG. 5F shows an embodiment which has inner and outer limiting curves751 and 752 which are similar to the curves 703 and 701 of FIG. 5Eexcept that a sine wave perturbation has been added to the two circles.Accordingly, it is seen that the inner and outer limiting curves may bearbitrarily selected to have any shape within the region of subsurfacesdescribed above. The embodiment of FIG. 5F has an aperture half angle of20° and the subsurfaces are represented by the coordinates listed inTable 12.

As with the other embodiments, the construction of these cavity shapesmay be simplified by relaxing the requirement that the aperture'sprojected solid angle be constant for certain portions of the cavitysurface. For example, the sidewall of the cavity between the inner andouter limiting curves 602 and 509 of FIG. 5C may be replaced by a smoothcylinder or alternatively, a cylinder having a uniform saw toothcross-section. In addition, the cylinder may extend beyond the sphere400 as shown in FIG. 4B, for example.

The manufacturing of blackbody simulators using the invention cavityshapes is conventional. Typical construction will involve a cylindricalsteel, graphite or ceramic core 101 as shown in FIG. 4D. Typical heatingmethods will be by the use of insulated nichrome wire 501 wrapped in aspiral around nearly all of the curved side of the cylindrical core. Oneor more temperature sensors 502, such as thermocouples or platinumresistance thermometers will be fitted into narrow cylindrical cavitieswhich will open to the opposite face of the cylinder from the cavityaperture. Insulation 505 will be used on all sides, and the entireassembly will be contained in an appropriate cylindrical or other shapedenclosure 503, with an opening provided to expose the cavity aperture.Insulation material and thickness will be determined by temperaturerequirements. Special vacuum type thermal insulation will be used forspace and space simulator applications. A fan 504 may be located in theopposite end of the enclosure from the aperture to provide cooling. Aconventional temperature controller controls the electric power to theheating wire 501 based on signals from a temperature sensor 502.

It will be obvious to those skilled in the art that the desirableproperties of the inventive cavity shapes may be obtained by minordeviations from the previously disclosed embodiments without departingfrom the scope of the invention. For instance, although the describedcavity shapes are formed from one or more smoothly curving subsurfaces,a cavity having a cross-section formed by short line segments closelyfollowing an embodiment's curving subsurfaces will result in a cavityshape having perhaps only minor or theoretical deficiencies from that ofthe computationally perfect cavity shape. Accordingly, the foregoingdescription and figures are illustrative only and are not meant to limitthe scope the invention, which is defined by the claims.

                  TABLE 1                                                         ______________________________________                                        S.sub.1    cavity surface                                                     s.sub.1    point on S.sub.1                                                   S.sub.2    surface having aperture as its perimeter                           s.sub.2    point on S.sub.2                                                   (x, y)     coordinates of point on S.sub.2                                    d = d(s.sub.1, s.sub.2)                                                                  distance between s.sub.1 and s.sub.2                               z          point on axis of symmetry                                                     z = 0 at aperture                                                             z = 1 at apex                                                      r = r(z)   cross-sectional radius at z                                        A.sub.0    apex half angle                                                    A.sub.1    angle formed by the normal to S.sub.1 at                                      s.sub.1, and the line between s.sub.1 and s.sub.2                  A'.sub.1   angle formed by the tangent to S.sub.1                                        at s.sub.1 and the axis of symmetry                                A.sub.2    angle formed by normal to S.sub.2 at s.sub.2                                  and the line between s.sub.1 and s.sub.2                           A'.sub.2   aperture half angle                                                D          diameter of aperture                                               L          depth of the cavity                                                M          specified maximum cross-sectional radius                           X          point on subsurface 402 where tangent                                         intersects rim of aperture                                         X'         point on subsurface 404 where r = M                                X"         point on subsurface 420 where tangent                                         intersects rim of aperture                                         X'"        point on subsurface 427 where tangent                                         intersects rim of aperture                                         ______________________________________                                    

                  TABLE 2                                                         ______________________________________                                        z            r       z            r                                           ______________________________________                                        1.00        .000     .50         .100                                         .95         .026     .45         .096                                         .90         .047     .40         .090                                         .85         .065     .35         .083                                         .80         .078     .30         .074                                         .75         .089     .25         .063                                         .70         .096     .20         .052                                         .65         .101     .15         .040                                         .60         .102 689 .10         .027                                         .59         .102 839 .05         .013 531                                     .58         .102 899 .04         .010 836                                     .57         .102 871 .03         .008 133                                     .56         .102 755 .02         .005 425                                     .55         .102 553 .01         .002 713                                     SMALL APERTURE EMBODIMENT (L = 1, A.sub.o = 30°)                       ______________________________________                                    

                  TABLE 3                                                         ______________________________________                                                             z value      Maximum                                     A.sub.o  A'.sub.2    For Maximum  Cross-                                      (Apex Half                                                                             (Aperture   Cross-Sectional                                                                            Sectional                                   Angle)   Half Angle) Radius       Radius                                      ______________________________________                                         7°                                                                             -3.5°                                                                              0.58         0.024                                       13°                                                                             -6.5°                                                                              0.58         0.044                                       20°                                                                             -10.1°                                                                             0.58         0.068                                       25°                                                                             -12.6°                                                                             0.58         0.085                                       30°                                                                             -15.2°                                                                             0.58         0.103                                       45°                                                                             -23.2°                                                                             0.58         0.159                                       60°                                                                             -31.8°                                                                             0.58         0.221                                       88°                                                                             -57.5°                                                                             0.56         0.404                                       89°                                                                             -61.7°                                                                             0.55         0.428                                        90°*                                                                           -90.0*       0.50*        0.500*                                     SUMMARY OF SMALL APERTURE EMBODIMENTS (L = 1)                                 ______________________________________                                         *NOTE:                                                                        The A.sub.o = 90° data is calculated for a sphere which is the         limiting case for large A.sub.o.                                         

                  TABLE 4a                                                        ______________________________________                                        x    y      x      y     x    y    x    y    x    y                           ______________________________________                                        -4   -1     -3     -2    -2   -3   -1   -4   0    -4                          -4   0      -3     -1    -2   -2   -1   -3   0    -3                          -4   1      -3     0     -2   -1   -1   -2   0    -2                                      -3     1     -2   0    -1   -1   0    -1                                      -3     2     -2   1    -1   0    0    0                                                    -2   2    -1   1    0    1                                                    -2   3    -1   2    0    2                                                              -1   3    0    3                                                              -1   4    0    4                           1    -4     2      -3    3    -2   4    -1                                    1    -3     2      -2    3    -1   4    0                                     1    -2     2      -1    3    0    4    1                                     1    -1     2      0     3    1                                               1    0      2      1     3    2                                               1    1      2      2                                                          1    2      2      3                                                          1    3                                                                        1    4                                                                        x-y COORDINATES FOR THE CENTERS OF A GRID OF                                  57 SQUARES                                                                    ______________________________________                                    

                  TABLE 4b                                                        ______________________________________                                        x-y COORDINATES FOR THE CENTERS OF A                                          GRID OF 61 HEXAGONS                                                           x       y       x         y      x       y                                    ______________________________________                                         ##STR1##                                                                             -2                                                                                     ##STR2## -2.5                                                                                  ##STR3##                                                                             -3                                    ##STR4##                                                                             -1                                                                                     ##STR5## -1.5                                                                                  ##STR6##                                                                             -2                                    ##STR7##                                                                             0                                                                                      ##STR8## -.5                                                                                   ##STR9##                                                                             -1                                    ##STR10##                                                                            1                                                                                      ##STR11##                                                                              .5                                                                                    ##STR12##                                                                            0                                     ##STR13##                                                                            2                                                                                      ##STR14##                                                                              1.5                                                                                   ##STR15##                                                                            1                                                     ##STR16##                                                                              2.5                                                                                   ##STR17##                                                                            2                                                                      ##STR18##                                                                            3                                     ##STR19##                                                                            -3.5    0         -4                                                                                    ##STR20##                                                                            -3.5                                  ##STR21##                                                                            -2.5    0         -3                                                                                    ##STR22##                                                                            -2.5                                  ##STR23##                                                                            -1.5    0         -2                                                                                    ##STR24##                                                                            -1.5                                  ##STR25##                                                                            -.5     0         -1                                                                                    ##STR26##                                                                            -.5                                   ##STR27##                                                                            .5      0         0                                                                                     ##STR28##                                                                            .5                                    ##STR29##                                                                            1.5     0         1                                                                                     ##STR30##                                                                            1.5                                   ##STR31##                                                                            2.5     0         2                                                                                     ##STR32##                                                                            2.5                                   ##STR33##                                                                            3.5     0         3                                                                                     ##STR34##                                                                            3.5                                                  0         4                                                    ##STR35##                                                                            -3                                                                                     ##STR36##                                                                              -2.5                                                                                  ##STR37##                                                                            -2                                    ##STR38##                                                                            -2                                                                                     ##STR39##                                                                              -1.5                                                                                  ##STR40##                                                                            -1                                    ##STR41##                                                                            -1                                                                                     ##STR42##                                                                              -.5                                                                                   ##STR43##                                                                             0                                    ##STR44##                                                                            0                                                                                      ##STR45##                                                                              .5                                                                                    ##STR46##                                                                            1                                     ##STR47##                                                                            1                                                                                      ##STR48##                                                                              1.5                                                                                   ##STR49##                                                                            2                                     ##STR50##                                                                            2                                                                                      ##STR51##                                                                              2.5                                                  ##STR52##                                                                            3                                                                     ______________________________________                                    

                  TABLE 5                                                         ______________________________________                                        z       r       A'.sub.1   z      r     A'.sub.1                              ______________________________________                                        1.000  .000     45.00°                                                                           .370   .134443                                                                              153.50°                        .950   .044     37.20     .390   .144   152.41                                .900   .077     30.53     .408   .154   151.21                                .850   .103     24.62     .489   .204   145.03                                .800   .123     19.27     .553   .254   138.66                                .750   .138     14.36     .604   .304   132.14                                .700   .149     9.83      .644   .354   125.44                                .650   .156     5.61      .675   .404   118.51                                .600   .159006  1.69      .698   .454   111.25                                .590   .159236  .94       .714   .504   103.51                                .580   .159335  .20       .722   .554   95.05                                 .570   .159307  -.53      .723   .564   93.24                                 .560   .159151  -1.25     .723   .574   91.38                                 .550   .158871  -1.96     .723628                                                                              .584443                                                                              89.47°                         .500   .156     -5.34     SUBSURFACE 404                                      .450   .150     -8.46     Subsurface 401 is a portion of                      .400   .141     -11.30    a sphere of radius .596 centered                    .390   .139     -11.83    at z = .594, r = o.0.                               .380   .137     -12.35    SUBSURFACE 401                                      .370   .134443  -12.86°                                                SUBSURFACE 402                                                                "THREE SURFACE" FINITE APERTURE EMBODIMENT                                    (A.sub.o = 45°, D = .1)                                                ______________________________________                                    

                  TABLE 6                                                         ______________________________________                                        z        r        z        r      z      r                                    ______________________________________                                        1.000   .000     .467222  .400008                                                                              .257074                                                                              .4000005                              .950    .116     .457     .398   .237   .387                                  .900    .180     .407     .386   .217   .373                                  .850    .224     .357     .369   .197   .358                                  .750    .281     .307     .347   .183261                                                                              .346611                               .700    .299     .300924  .344144                                             .650    .311     SUBSURFACE 420                                                                              SUBSURFACE 429                                 .600    .317133  .300924  .344114                                                                              .183261                                                                              .346611                               .590    .317852  .306     .354   .186   .357                                  .580    .318382  .311     .364   .192   .377                                  .570    .318724  .316     .374   .196   .397                                  .560    .318882  .325     .394   .196071                                                                              .400000                               .550    .318856  .326748  .400008                                             .540    .318648  SUBSURFACE 425                                                                              SUBSURFACE 430                                 .530    .318261  .326748  .400008                                                                              .196071                                                                              .400000                               .520    .317695  .307     .390   .176   .384                                  .510    .316953  .287     .380   .156   .366                                  .500    .316035  .267     .369   .136   .347                                  .450    .309     .247     .356   .126   .336                                  .420    .303     .239917  .351695                                                                              .112448                                                                              .321363                               .410    .300     SUBSURFACE 427                                                                              SUBSURFACE 431                                 .404    .298554  .239917  .351695                                                                              .112448                                                                              .321363                               SUBSURFACE 402                                                                             .244     .362     .116   .341                                       .404146                                                                            .298554  .251     .382   .117   .361                                  .412    .309     .255     .392   .117212                                                                              .381363                               .446    .359     .257074  .400005                                               .467222                                                                             .400008  SUBSURFACE 428                                                                              SUBSURFACE 432                                 SUBSURFACE 404                                                                Subsurface 401 is a sphere of radius .525                                     centered at z = .489, r = 0.0 -FRESNEL CAVITY SHAPE EMBODIMENT (A.sub.o =     76.5°,                                                                 D = .385, M = .40)                                                            ______________________________________                                    

                  TABLE 7                                                         ______________________________________                                        z         r             z      r                                              ______________________________________                                        1.000     0.000         .591   .600                                           .890      .021          .481   .523                                           .758      .037          .379   .439                                           .894      .067          .431   .519                                           .995      .097          .476   .600                                           .865      .108          .386   .520                                           .746      .111          .306   .438                                           .870      .151          .348   .518                                           .992      .201          .384   .600                                           .842      .199          .304   .513                                           .719      .188          .232   .421                                           .853      .248          .268   .511                                           .993      .328          .295   .600                                           .813      .307          .215   .491                                           .668      .275          .147   .376                                           .812      .365          .177   .496                                           .989      .515          .187   .600                                           .769      .460                                                                .562      .375                                                                .680      .485                                                                .778      .600                                                                .598      .513                                                                .459      .424                                                                .531      .514                                                                EMBODIMENT OF FIG. 5A                                                         ______________________________________                                    

A portion of a circle of radius 1.054 extends from the last point to theedge of the aperture to define subsurface 401. The center of the circleis on an extension of the axis 1.049 from the aperture and 0.049 outpast the apex. The radius of the aperture is 0.1 for an L/R ratio of10:1. The apex half-angle is 13.

                  TABLE 8                                                         ______________________________________                                        z         r             z      r                                              ______________________________________                                        1.000     0.000         .658   .401                                           .860      .030          .741   .481                                           .722      .046          .621   .434                                           .846      .076          .505   .376                                           .939      .106          .593   .466                                           .819      .116          .692   .596                                           .708      .116          .552   .522                                           .798      .146          .397   .414                                           .895      .186          .461   .504                                           .785      .184          .516   .600                                           .687      .176          .416   .523                                           .757      .206          .307   .420                                           .857      .256          .355   .509                                           .757      .246          .393   .600                                           .660      .230          .303   .508                                           .752      .280          .218   .401                                           .831      .330          .252   .491                                           .721      .308          .281   .600                                           .621      .282          .201   .493                                           .698      .332          .113   .338                                           .789      .402          .126   .398                                           .679      .371          .137   .518                                           .571      .331                                                                EMBODIMENT OF FIG. 5B                                                         ______________________________________                                    

A portion of a circle of radius 0.985 extends from the last point to theedge of the aperture to define subsurface 401. The center of the circleis on the axis a distance 0.980 from the aperture in the direction ofthe apex. The radius of the aperture is 0.1 for an L/R ratio of 10:1.The apex half-angle is 15°.

                  TABLE 9                                                         ______________________________________                                        z         r             z      r                                              ______________________________________                                        1.000     0.000         .919   .517                                           .933      .022          .990   .644                                           .850      .042          .782   .623                                           .926      .068          .575   .550                                           .992      .096          .603   .603                                           .913      .113          .623   .650                                           .848      .123          .525   .602                                           .930      .160          .442   .550                                           .991      .195          .465   .605                                           .911      .205          .479   .651                                           .849      .209          .405   .600                                           .910      .245          .343   .549                                           .990      .304          .359   .607                                           .880      .308          .367   .650                                           .848      .307          .313   .605                                           .911      .357          .258   .550                                           .990      .438          .262   .569                                           .921      .438          .266   .629                                           .849      .432                                                                EMBODIMENT OF FIG. 5C                                                         ______________________________________                                    

A portion of a circle of radius 0.858 extends from the last point to theedge of the aperture to define subsurface 401. The center ofthe circleis on the axis a distance 0.852 from the aperture in a direction towardthe apex. The radius of the aperture is 0.1 for an L/R ratio 10:1. Theapex half-angle is 20°.

                  TABLE 10                                                        ______________________________________                                        z         r             z      r                                              ______________________________________                                        1.000     0.000         .694   .385                                           .915      .028          .750   .442                                           .829      .049          .793   .495                                           .895      .071          .734   .482                                           .952      .096          .663   .462                                           .873      .111          .711   .526                                           .800      .121          .753   .597                                           .864      .149          .686   .577                                           .919      .177          .611   .550                                           .850      .184          .635   .593                                           .774      .187          .659   .650                                           .835      .220          .558   .608                                           .889      .254          .455   .549                                           .819      .255          .475   .595                                           .747      .252          .492   .650                                           .806      .290          .417   .602                                           .858      .331          .350   .550                                           .778      .325          .366   .608                                           .723      .317          .373   .651                                           .777      .361          .311   .601                                           .828      .409          .258   .549                                           .768      .401          .265   .618                                           EMBODIMENT OF FIG. 5D                                                         ______________________________________                                    

A portion of a circle of radius 0.838 extends from the last point to theedge of the aperture to define subsurface 401. The center of the circleis on the axis a distance 0.832 from the aperture measured in adirection toward the apex. The radius of the aperture is 0.1 for an L/Rratio of 10:1. The apex half-angle is 21°.

                  TABLE 11                                                        ______________________________________                                        z         r                    r                                              ______________________________________                                        1.000     0.000         .708   .433                                           .924      .024          .606   .400                                           .846      .043          .653   .451                                           .922      .069          .705   .517                                           .993      .100          .611   .482                                           .925      .114          .512   .435                                           .830      .128          .560   .499                                           .903      .161          .600   .566                                           .967      .197          .503   .515                                           .878      .206          .405   .449                                           .798      .208          .440   .510                                           .867      .248          .479   .595                                           .926      .289          .382   .525                                           .836      .289          .286   .435                                           .751      .282          .316   .509                                           .816      .328          .341   .597                                           .870      .375          .250   .505                                           .771      .364          .156   .377                                           .685      .346          .169   .426                                           .745      .399          .181   .535                                           .796      .452                                                                EMBODIMENT OF FIG. 5E                                                         ______________________________________                                    

A portion of a circle of radius 0.858 extends from the last point to theedge of the aperture to define subsurface 401. The center of the circleis located on the axis a distance 0.852 from the aperture measured in adirection toward the apex. The radius of the aperture is 0.1 for an L/Rratio of 10:1. The apex half-angle is 20°.

                  TABLE 12                                                        ______________________________________                                        z         r             z      r                                              ______________________________________                                        1.000     0.000         .771   .456                                           .943      .188          .717   .443                                           .879      .357          .750   .480                                           .927      .051          .779   .518                                           .973      .070          .711   .501                                           .915      .083          .654   .482                                           .846      .095          .679   .514                                           .902      .118          .707   .557                                           .943      .137          .632   .530                                           .884      .146          .570   .502                                           .820      .152          .597   .544                                           .874      .177          .618   .581                                           .922      .204          .528   .536                                           .862      .208          .442   .482                                           .804      .209          .467   .526                                           .856      .239          .489   .572                                           .906      .272          .399   .509                                           .856      .272          .323   .444                                           .794      .270          .353   .508                                           .852      .309          .371   .556                                           .891      .340          .305   .495                                           .841      .338          .237   .420                                           .781      .332          .257   .476                                           .820      .363          .277   .556                                           .867      .407          .224   .495                                           .807      .400          .169   .419                                           .758      .392          .177   .458                                           .794      .426          .184   .540                                           .830      .467                                                                EMBODIMENT OF FIG. 5F                                                         ______________________________________                                    

A portion of a circle of radius 0.858 extends from the last point of thetable to the edge of the aperture to define subsurface 401. The centerof this circle is on the axis a distanc 0.852 from the aperture measuredin the direction toward the apex. The radius of the aperture is 0.1 foran L/R ratio of 10:1. The apex half-angle is 20°.

I claim:
 1. A blackbody simulator, comprising:a core with a first side;the core having an aperture on its first side to a cavity, the cavitybeing rotationally symmetrical about an axis and having a cone-like apexon the axis opposite the aperture with an apex half-angle of less that60°; the cavity surface being shaped so that the value of the projectedsolid angle of the aperture with respect to any point on the cavitysurface is generally constant; the cavity having n subsurfaces with then^(th) subsurface having the shape of a portion of a sphere; the cavitysubsurfaces defining inner and outer limiting curves with eachsubsurface up to the (n-1)^(th) subsurface arcuately extending from theinner limiting curve to the outer limiting curve; said outer limitingcurve remaining inside the sphere defined by the n^(th) subsurface andthe inner limiting curve remaining outside an arch defined by thelocations at which a tangent in a plane containing the axis of symmetryintersects the rim of the aperture for each subsurface if extended tothe arch.
 2. The simulator of claim 1, wherein a portion of thesubsurfaces away from the axis of symmetry are replaced by a cylinder.3. A blackbody simulator, comprising:a core with a first side; the corehaving an aperture on its first side to a cavity, the cavity beingrotationally symmetrical about an axis and having a cone-like apex onthe axis opposite the aperture, the cavity surface shaped so that thevalue of the projected solid angle of the aperture with respect to anypoint on the cavity surface is generally constant, and the cavity havingn subsurfaces; the first subsurface arcuately extending from the apextoward the aperture to a circular junction with a second subsurface atwhich place a tangent to the first subsurface in a plane containing theaxis of symmetry intersects the rim of the aperture; the secondsubsurface arcuately extending from the junction with the firstsubsurface to a circular junction with a third subsurface at whichjunction the distance of points on the second subsurface from a planedefined by the aperture reaches a specified maximum value N; the thirdsubsurface arcuately extending from the circular junction with thesecond subsurface toward the aperture to a circular junction with afourth subsurface at which junction a tangent to the third subsurface ina plane containing the axis of symmetry intersects the rim of theaperture; a fourth, fifth, sixth, seventh, up to n^(th) subsurfacecontinuing until the (n-1)^(th) subsurface intersects the n^(th)subsurface, said n^(th) subsurface arcuately extending from the rim ofthe aperture, and said n^(th) subsurface having the shape of a portionof a sphere; said n being an integer from 5 to about 1,000, said fourth,sixth, up to r^(th) subsurface arcuately extending from the circularjunction with the previous subsurface to a circular junction with thenext subsurface at which junction the distance of points on said fourth,sixth, up to r^(th) subsurface from the aperture plane reaches the samespecified maximum value N, as that specified for the second subsurface;the (r+2)^(th), (r+4)^(th), up to (n-1)^(th) subsurface arcuatelyextending from the circular junction with the previous subsurface to acircular junction with the next subsurface at which junction thedistance of points on said (r+2)^(th), (r+4)^(th), up to (n-1)^(th)subsurface from the axis of symmetry reaches a specified maximum valueM; said r being an integer from 4 to about 1,000, said third, fifth,seventh, up to m^(th) subsurface arcuately extending from the circularjunction with the previous subsurface to a circular junction with thenext subsurface at which junction a tangent to said third, fifth,seventh, up to m^(th) subsurface in a plane containing the axis ofsymmetry intersects the rim of the aperture; and said m being an integerfrom 3 to about 1,000.
 4. A blackbody simulator, comprising:a corehaving a first side; the core further having a cavity and an aperture onits first side to the cavity, the cavity being rotationally symmetricalabout an axis and having a cone-like apex on the axis opposite theaperture with an apex half-angle of less than 60° the cavity surfacebeing shaped so that the value of the projected solid angle of theaperture with respect to any point on the cavity surface issubstantially constant; the cavity surface comprising n subsurfaces; thefirst subsurface extending from the apex toward the aperture to acircular junction with the second subsurface; the n^(th) subsurfaceextending from the rim of the aperture, and said n^(th) subsurfacehaving the shape of a portion of a sphere; said n being an integer from5 to about 1,000; the cavity subsurfaces defining inner and outerlimiting curves with each subsurface up to the (n-1)^(th) subsurfaceextending from the inner limiting curve to the outer limiting curve;said outer limiting curve remaining inside the sphere defined by then^(th) subsurface and the inner limiting curve remaining outside an archdefined by the locations at which a tangent in a plane containing theaxis of symmetry intersects the rim of the aperture for each subsurfaceif extended to the arch.
 5. For use in a system requiringelectromagnetic radiation to be radiated onto a utilization object, ablackbody simulator having a cavity defining an apex and a cavitysurface, and an aperture to the cavity, said cavity surface beingdivided into a primary radiating surface and a secondary radiatingsurface, the primary radiating surface comprising portions of the cavitysurface which are in direct line of sight to some portion of theutilization object through the aperture, the secondary radiating surfacecomprising portions of the cavity surface which are not part of theprimary radiating surface;wherein the projected solid angle of theaperture with respect to substantially all portions of the primaryradiating surface is substantially constant; and the primary radiatingsurface comprises a flat circular plate having concentric circulargrooves, and the secondary radiating surface comprises a cylinder and aflat disc aperture plate.
 6. A blackbody simulator comprising:a corehaving a first side; the core further having a cavity and an aperture onits first side to the cavity, the cavity being rotationally symmetricalabout an axis and having a cone-like apex on the axis opposite theaperture with an apex half-angle of less than 60°, a substantial portionof the cavity surface being shaped so that the value of the projectedsolid angle of the aperture with respect to any point on the cavitysurface portion is substantially constant; the cavity surface portioncomprising at least n subsurfaces; the first subsurface extending fromthe apex toward the aperture; said n being an integer from 5 to about1,000; a substantial number of said cavity portion subsurfaces defininginner and outer limiting curves with each of said substantial number ofsubsurfaces extending from the inner limiting curve to the outerlimiting curve; said outer limiting curve remaining inside a spherecontaining the rim of the aperture and having a radius such that thevalue of the projected solid angle of the aperture with respect to anypoint of the sphere is substantially constant, and said inner limitingcurve remaining outside an arch defined by the locations at which atangent in a plane containing the axis of symmetry intersects the rim ofthe aperture for each subsurface if extended to the arch.
 7. For use ina system requiring electromagnetic radiation to be radiated onto autilization object, a blackbody simulator having a cavity defining anapex and a cavity surface, and an aperture to the cavity, said cavitysurface being divided into a primary radiating surface and a secondaryradiating surface, the primary radiating surface comprising portions ofthe cavity surface which are in direct line of sight to some portion ofthe utilization object through the aperture, the secondary radiatingsurface comprising portions of the cavity surface which are not part ofthe primary radiating surface;wherein the projected solid angle of theaperture with respect to all portions of the primary radiating surfaceis generally constant; and the primary radiating surface comprises aflat circular plate having concentric circular grooves.
 8. A blackbodysimulator according to claim 6 wherein the outer limiting curvecomprises a straight line outer limiting curve passing through the apexand the inner limiting curve comprises a straight line inner limitingcurve parallel to the straight line outer limiting curve.
 9. Thesimulator of claim 6 or 8 wherein a second portion of the cavity surfaceaway from the axis of symmetry is a substantially cylindrical surface.10. A blackbody simulator according to claim 4 wherein the outerlimiting curve comprises a first straight line outer limiting curve anda second straight line outer limiting curve;and wherein the innerlimiting curve includes an arch defined by the locations on thesubsurfaces at which a tangent in a plane containing the axis ofsymmetry intersects the rim of the aperture for each subsurface; saidfirst straight line outer limiting curve passing through the apex andsaid second straight line outer limiting curve being parallel to theaxis of symmetry and a distance M from said axis of symmetry.
 11. Ablackbody simulator according to claim 4 wherein the outer limitingcurve comprises a first straight line outer limiting curve and a secondstraight line outer limiting curve;and wherein the inner limiting curvecomprises a first straight line inner limiting curve and a secondstraight line inner limiting curve; said first straight line outerlimiting curve passing through the apex perpendicular to the axis ofsymmetry; said second straight line outer limiting curve being parallelto the axis of symmetry and a distance M from said axis of symmetry;said first straight line inner limiting curve being perpendicular to theaxis of symmetry intersecting the axis of symmetry a distance P from theaperture; said second straight line inner limiting curve being parallelto the axis of symmetry and a distance O from said axis of symmetry. 12.A blackbody simulator according to claim 4 wherein the outer limitingcurve comprises a first straight line outer limiting curve and a secondstraight line outer limiting curve;and wherein the inner limiting curvecomprises a first straight line inner limiting curve and a secondstraight line inner limiting curve; said first straight line outerlimiting curve passing through the apex at an oblique angle; said secondstraight line outer limiting curve being parallel to the axis ofsymmetry and a distance M from said axis of symmetry; said firststraight line inner limiting curve being parallel to the first straightline outer limiting curve and intersecting the axis of symmetry adistance P from the aperture; said second straight line inner limitingcurve being parallel to the axis of symmetry and a distance O from saidaxis of symmetry.
 13. A blackbody simulator according to claim 4 whereinthe inner and outer limiting curves are concentric circles with theircenter on the axis of symmetry.
 14. A blackbody simulator according toclaim 9 wherein the aperture defines a plane and the cylindrical surfaceextends to the plane of the aperture, and wherein the cavity has a thirdsurface which is a plane surface in the plane of the aperture.
 15. Ablackbody simulator according to claim 5 wherein the cylindrical surfaceis threaded.
 16. A blackbody simulator according to claim 14 wherein thecylindrical surface is threaded.
 17. A blackbody simulator according toclaim 8 wherein a second portion on the cavity surface has an axialcrossection approximating a sawtooth shape.
 18. A blackbody simulatoraccording to claim 6 wherein a second portion of the cavity surface awayfrom the axis of symmetry has an axial crossection approximating asawtooth shape.
 19. A blackbody simulator according to claim 7 whereinthe secondary radiating surface comprises a cylinder and a subsurfacearcuately extending from the rim of the aperture to the cylinder, saidsubsurface having the shape of a portion of a sphere, and saidsubsurface being shaped so that the value of the projected solid angleof the aperture with respect to any point on the subsurface issubstantially equal to the value of the projected solid angle of theaperture with respect to points on the cavity primary radiating surfacenear the apex.
 20. A blackbody simulator according to claim 5 whereinthe cylinder has a threaded surface.
 21. A blackbody simulator accordingto claim 19 wherein the cylinder has a threaded surface.
 22. A blackbodysimulator according to claim 5 wherein the cylinder has a surface whichhas an axial crossection which approximates a sawtooth shape.
 23. Ablackbody simulator according to claim 19 wherein the cylinder has asurface which has an axial crossection which approximates a sawtoothshape.
 24. A blackbody simulator according to claim 4 or 11 wherein atleast one subsurface comprises a plurality of subsurfaces having anaxial cross-sectional shape of straight line segments.
 25. A blackbodysimulator according to claim 5 wherein at least one groove comprises aplurality of subsurfaces having an axial cross-sectional shape ofstraight line segments.
 26. The simulator of claim 6, wherein a secondportion of the cavity surface away from the axis of symmetry has theshape of a cylinder.
 27. A blackbody simulator according to claim 6 foruse in a system requiring electromagnetic radiation to be radiated ontoa utilization object, wherein the cavity surface comprises a primaryradiating surface and a secondary radiating surface, the primaryradiating surface comprising all portions of the cavity surface whichare in direct line of sight to some portion of the utilization objectthrough the aperture;and wherein said substantial portion of the cavitysurface comprises said primary radiating surface.
 28. The simulator ofclaim 27, wherein a portion of the secondary surface has a cylindricalshape.
 29. A blackbody simulator according to claim 6 wherein the outerlimiting curve comprises a first straight line outer limiting curve anda second straight line outer limiting curve;and wherein the innerlimiting curve includes an arch defined by the locations on thesubsurfaces at which a tangent in a plane containing the axis ofsymmetry intersects the rim of the aperture for each subsurface; saidfirst straight line outer limiting curve passing through the apex andsaid second straight line outer limiting curve being parallel to theaxis of symmetry.
 30. A blackbody simulator according to claim 6 whereinthe outer limiting curve comprises a first straight line outer limitingcurve and a second straight line outer limiting curve;and wherein theinner limiting curve comprises a first straight line inner limitingcurve and a second straight line inner limiting curve; said firststraight line outer limiting curve passing through the apexperpendicular to the axis of symmetry; said second straight line outerlimiting curve being parallel to the axis of symmetry; said firststraight line inner limiting curve being perpendicular to the axis ofsymmetry; and said second straight line inner limiting curve beingparallel to the axis of symmetry.
 31. A blackbody simulator according toclaim 6 wherein the outer limiting curve comprises a first straight lineouter limiting curve and a second straight line outer limiting curve;andwherein the inner limiting curve comprises a first straight line innerlimiting curve and a second straight line inner limiting curve; saidfirst straight line outer limiting curve passing through the apex at anoblique angle; said second straight line outer limiting curve beingparallel to the axis of symmetry; said first straight line innerlimiting curve being parallel to the first straight line outer limitingcurve and intersecting the axis of symmetry; and said second straightline inner limiting curve being parallel to the axis of symmetry.
 32. Ablackbody simulator according to claim 6 wherein the inner and outerlimiting curves are concentric circles with their center on the axis ofsymmetry.
 33. A blackbody simulator according to claim 27 wherein theouter limiting curve of the primary radiating surface comprising astraight line outer limiting curve passing through the apex at anoblique angle and the inner limiting curve of the primary radiatingsurface comprises a straight line inner limiting curve which is parallelto the first straight line outer limiting curve and intersects the axisof symmetry.
 34. A blackbody simulator according to claim 33 whereinsaid secondary radiating surface comprises a cylindrical surface.
 35. Ablackbody simulator according to claim 34 wherein the aperture defines aplane and the cylindrical surface is extended to the plane of theaperture, and the secondary radiating surface further comprises a planesurface in the plane of the aperture.
 36. A blackbody simulatoraccording to claim 34 wherein the cylindrical surface is threaded.
 37. Ablackbody simulator according to claim 35 wherein the cylindricalsurface is threaded.
 38. A blackbody simulator according to claim 33wherein a portion of the secondary radiating surface has an axialcross-section which approximates a sawtooth shape.
 39. A blackbodysimulator according to claim 27 wherein the primary radiating surfacecomprises a flat circular plate having concentric circular grooves. 40.A blackbody simulator according to claim 39 wherein the secondaryradiating surface comprises a cylinder.
 41. A blackbody simulatoraccording to claim 40 wherein the secondary radiating surface furthercomprises a flat disc in the plane of the aperture.
 42. A blackbodysimulator according to claim 40 wherein the secondary radiating surfacefurther comprises a subsurface arcuately extending from the rim of theaperture to the cylinder, said subsurface having the shape of a portionof a sphere, and said subsurface being shaped so that the value of theprojected solid angle of the aperture with respect to any point on thespherical subsurface is substantially equal to the value of theprojected solid angle of the aperture with respect to points on thecavity surface near the apex.
 43. A blackbody simulator according toclaim 40 wherein the cylinder has a threaded surface.
 44. A blackbodysimulator according to claim 39 wherein a portion of the secondaryradiating surface has an axial crossection which approximates a sawtoothshape.